New results are presented concerning the state isomorphism approach to global identifiability analysis of parameterized classes of nonlinear homogeneous systems with specified initial states. For such systems, the local state isomorphism for a pair of indistinguishable parameter vectors is homogeneous of degree one. Under certain conditions, which may only be satisfied for homogeneous polynomial systems, the local state isomorphism is linear. Here, the key issue is whether or not the observability rank condition holds at the origin. The controllability rank condition is shown to play a truly secondary role. The results are generalized to the multivariable case and a worked example demonstrates how identifiability analysis may be simplified along these lines.

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Keywords Controllability, Identifiability, Nonlinear systems, Observability
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Conference IFAC Symposium on System Identification
Peeters, R, & Hanzon, B. (2003). Identifiability of nonlinear homogeneous polynomial systems. In IFAC-PapersOnLine (pp. 729–734). doi:10.1016/S1474-6670(17)34848-6